2017/04/30 by Thomas Dreyfus, Alberto Lastra, Stéphane Malek
Mathematics · #math.CA #math.AP #math.CV #msc:35C10 #msc:35C20
paper · pdf · doi:10.1186/s13662-019-2263-5
published as Advances in Difference Equations, 2019.1 (2019): 326 · arXiv admin note: text overlap with arXiv:1508.02621
arxiv created 2021/01/21 · arxiv updated 2021/01/22
The analytic and formal solutions of certain family of q-difference-differential equations under the action of a complex perturbation parameter is considered. The previous study of the last two authors provides information in the case when the main equation under study is factorizable, as a product of two equations in the so-called normal form. Each of them gives rise to a single level of q-Gevrey asymptotic expansion. In the present work, the main problem under study does not suffer any factorization, and a different approach is followed. More precisely, we lean on the technique developed in a paper, where the first author makes distinction among the different q-Gevrey asymptotic levels by successive applications of two q-Borel-Laplace transforms of different orders both to the same initial problem and which can be described by means of a Newton polygon.